THEORETICAL STUDIES RELATED TO THE DETERMINATION OF SEISMIC ENERGY SOURCE DEPTH

This report summarizes work on a number of different but related topics, as folows: The effect of seismic source depth on Rayleigh wave spectra is examined for a dissipative half space and for an elastic layer overlying an elastic half space. In the two-layer earth model, the higher-mode amplitude spectra increase relative to the fundamental as the source approaches the base of the crust. The exact ray theory and matrix method are in principle devices for obtaining the response of a layered system over a limited time interval. Both methods prove to be inefficient from the standpoint of automatic computation but useful in analyzing certain general properties of the response functions in multilayered systems. Geometric ray theory is used to study the effects of layer thickness and range on the refracted arrival along a high-speed layer embedded in an infinite medium. The reflection of a plane compressional wave at a plane interface is analyzed with particular emphasis on the equation for continuity of the instantaneous energy flux. Inside the critical angle, Knott's equation gives continuity of the instantaneous flux, but beyond the critical angle Knott's equation must be replaced by three separate conditions. Rept. on Proj. VELA-UNIFORM.